Compressing textures
If all you need to do is save space to transfer the file, you can try a couple things.

Compress the blend file with textures (zip, xz, etc)
Create a tarball with your textures, and use compression across multiple files. This takes advantage of the fact that textures contain very redundant information.

If you need to save space and still want everything to work normally, your only option is to really use lower-res textures. Although you could probably use a lossy format like jpeg as opposed to png another lossless compression algorithm if you're okay with some quality loss.